Optimizes neural network training by dynamically updating Tucker decomposition ranks.
problem Redundant parameters in neural network architectures.
method Geometry-aware training of factorized layers in tensor Tucker format.
result Optimal locally approximating the original dynamics without initial rank knowledge.
A new method for efficient neural network fine-tuning using queryable low-rank update atoms.
problem Rigidity of static low-rank adaptation methods when input and depth-wise computation vary.
method A shared queryable memory of low-rank update atoms, allowing dynamic and context-sensitive adaptation.
result Improves final test performance and training stability compared to standard low-rank adaptation.
PSI-LinUCB improves scalability for large recommender systems.
problem Efficiently training and inferring for large action spaces in recommender systems.
method Represent inverse design matrix as diagonal + low-rank correction, derive stable rank-1 and batched updates, use projector-splitting integrator.
result Demonstrated effectiveness on recommender system datasets, achieving scalable training and inference.
Flora uses random projections to achieve high-rank updates with low memory usage.
problem Excessive memory usage in large neural networks during training.
method Flora approximates LoRA using random projections to enable high-rank updates with sublinear space complexity.
result Flora achieves high-rank updates with significantly reduced memory usage compared to LoRA.
New method finds efficient low-rank neural networks during training.
problem High memory and computational demands of neural networks.
method Restricts weight matrices to a low-rank manifold and updates low-rank factors.
result Significantly reduced time and memory resources required for training and evaluation.
A new method for efficiently updating large-scale matrices in real-time.
problem Updating large-scale matrices with evolving data in real-time.
method Incremental SVD approach that handles row/column appends, rank-1 updates, and refresh strategies.
result Incremental SVD achieves accuracy close to full SVD with a fraction of the computational cost.
A new method reduces high-dimensional filtering to quadratic complexity.
problem High-dimensional dynamical systems inference and simulation.
method Low-rank Kalman filtering using dynamical low-rank integrator.
result The method reproduces exact Kalman filter in low-rank limit.
SGD updates align with a low-rank subspace but do not lead to further loss reduction.
problem Understanding the training dynamics of deep neural networks, particularly the role of the dominant subspace.
method Exploring whether neural networks can be trained within the dominant subspace of the loss Hessian.
result SGD updates, when projected onto the dominant subspace, do not decrease the training loss further, suggesting spurious alignment.
Muon replaces matrix gradient with polar factor, optimizing flat spectrum updates
problem Optimization bias in matrix updates
method Using polar factor of gradient
result Muon update maximizes entropy among bounded updates
FedLoRU improves FL efficiency by using low-rank updates.
problem Communication inefficiency and performance reduction in Federated Learning.
method Proposes FedLoRU, a low-rank update framework for FL, which reduces communication costs while maintaining performance.
result FedLoRU achieves convergence rates similar to FedAvg and is robust to heterogeneous and large numbers of clients.
GeLoRA optimizes LoRA fine-tuning by dynamically adjusting ranks based on intrinsic dimensionality.
problem Efficient fine-tuning of large language models with limited computational resources.
method GeLoRA computes intrinsic dimensionality to adaptively select LoRA ranks, balancing expressivity and efficiency.
result GeLoRA consistently outperforms recent baselines within the same parameter budget on multiple tasks.
Develops efficient method for updating models with small data changes.
problem Efficiently updating models when data changes (e.g., adding/removing instances/features).
method Generalized Low-Rank Update (GLRU) for non-linear estimators.
result Provides updated solutions with computational complexity proportional to dataset changes.
New algorithm for maximizing submodular functions in real-time data changes.
problem Maximizing submodular functions under dynamic constraints.
method Randomized algorithm with O(k2) amortized update time. result 4-approximate solution to submodular maximization problem.
Develops a regression model for partially observed dynamic tensor data.
problem Characterizing the relationship between dynamic tensor data and external covariates when data is only partially observed.
method Introduces low-rank, sparsity, and fusion structures on the regression coefficient tensor, and uses a loss function projected over observed entries. Developed an efficient non-convex alternating updating algorithm.
result Derived finite-sample error bounds for the estimator.
Sparsity and low-rank models have been popular for reconstructing images and videos from limited or corrupted measurements. Dictionary or transform learning methods are useful in applications such as denoising, inpainting, and medical image reconstruction. This paper proposes a framework for online (or time-sequential)…
New method prevents forgetting in LLMs by dynamically identifying task-specific subspaces.
problem Catastrophic forgetting in continual learning of LLMs.
method Adaptive Singular Value Decomposition (SVD) for constrained full fine-tuning.
result Achieves state-of-the-art results in continual learning benchmarks.
New PFPPs based on rank-dependent utility for better performance control.
problem Improving performance prediction in systems with short-term control.
method Introduces rank-dependent PFPPs, solves integral equations via Volterra theory.
result Existence of rank-dependent PFPPs under specific market conditions.
A new method learns complex dynamical systems from data efficiently.
problem Learning complex dynamical systems from large-scale data efficiently.
method Low-rank structured variational autoencoding framework for nonlinear Gaussian state-space models.
result Consistently demonstrates better predictive capabilities compared to other models.
Most of real-world graphs are dynamic, i.e., they change over time by a sequence of update operations. While the regression problem has been studied for static graphs and temporal graphs, it is not investigated for general dynamic graphs. In this paper, we study regression over dynamic graphs. First, we present the not…
PLUMAGE improves large model training efficiency and stability.
problem Accelerator memory and networking constraints during large model training.
method Probabilistic Low rank Unbiased Minimum Variance Gradient Estimator (PLUMAGE) that resolves bias and variance issues.
result PLUMAGE reduces training loss by 28% on average across the GLUE benchmark.
New method improves compatibility of risk stratification models without sacrificing accuracy.
problem Compatibility issues arise when updating clinical machine learning models.
method Proposes rank-based compatibility measure and new loss function.
result Increased compatibility of models by 0.019 with no loss in discriminative performance.
Proposes PredVAR model for reduced-dimensional dynamics from noisy data.
problem Extracting low-dimensional dynamics from high-dimensional noisy data.
method Probabilistic reduced-dimensional vector autoregressive model with oblique projection.
result Iterative algorithm yields dynamic latent variables with rank-ordered predictability.
QSurv models survival data without discretization, achieving high accuracy.
problem Intractable likelihood estimation for continuous-time survival models.
method QSurv uses numerical quadrature for cumulative hazard approximation and time-conditioned low-rank adaptation.
result QSurv achieves competitive predictive performance and interpretable hazard patterns.
The paper analyzes dynamics of momentum in high dimensions with sparse updates.
problem Theoretical analysis of momentum dynamics in high-dimensional sparse settings.
method Theoretical analysis of two models: least squares with sparse inputs and logistic regression with a rare class.
result Characterization of high-dimensional limits of momentum dynamics and phase structure.
Hyperfitting improves LLM generation quality by enhancing diversity, contrary to simple temperature scaling.
problem Improving open-ended generation quality of LLMs with minimal fine-tuning effort.
method Demonstrates that hyperfitting, a phenomenon where LLMs are fine-tuned to near-zero training loss, enhances generation quality and mitigates repetition.
result Hyperfitting is distinct from temperature scaling and involves a dynamic, context-dependent rank reordering mechanism in the final transformer block.
Paper proposes recycling model updates in federated learning by exploiting low-rank gradient subspaces.
problem Large parameter transmissions in federated learning.
method Look-back Gradient Multiplier (LBGM) algorithm exploiting low-rank property of gradient subspaces.
result LBGM reduces communication overhead with minimal performance loss.
In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-1 update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence g…
New algorithm optimizes MCMC sampling for structural dynamic models.
problem Time-consuming retraining of neural networks in MCMC methods.
method Adaptive meta-learning SGHMC algorithm that optimizes sampling strategy.
result Trained sampler can be applied to various problems without retraining.
Paper presents a rank-1 approximation method for natural policy gradients in deep RL.
problem Computing natural gradients requires inverting the Fisher Information Matrix, which is computationally expensive.
method Develops a rank-1 approximation to the inverse Fisher Information Matrix for efficient natural policy optimization.
result The rank-1 approximation converges faster and has similar sample complexity to stochastic policy gradient methods.
Improves BBVI for high-dimensional Gaussian approximations by using low-rank approximations.
problem Scalability issues with BBVI for high-dimensional multivariate Gaussian approximations.
method Extends BaM framework to handle full covariance matrices by integrating patch step for low-rank parameterization.
result Shows improved efficiency and scalability on synthetic and real-world high-dimensional inference problems.
Improved tensor GLM estimation for complex data.
problem Complex tensor data in GLMs leads to high-dimensional, ill-posed estimation.
method Proposed LSRTR-M algorithm using Muon updates for faster convergence and lower errors.
result LSRTR-M converges faster and achieves lower errors than LSRTR.
This work investigates implicit bias in multiclass separable data using a novel geometry-aware optimizer.
problem Understanding implicit bias in overparameterized models on multiclass separable data.
method Introduces NucGD, a geometry-aware optimizer enforcing low-rank structures through nuclear norm constraints.
result NucGD enables scalable training and characterizes the impact of stochastic optimization dynamics.
We present a framework for supervised subspace tracking, when there are two time series xt and yt, one being the high-dimensional predictors and the other being the response variables and the subspace tracking needs to take into consideration of both sequences. It extends the classic online subspace tracking work…
LR-EDNN reduces PDE solver complexity by limiting network weights to low-rank subspace.
problem Efficiently solving time-dependent PDEs with deep neural networks.
method Low-rank constraint on network weights using SVD for efficient parameter updates.
result LR-EDNN achieves comparable accuracy to full EDNN with fewer parameters and lower cost.
Proposes a probabilistic digital twin for dynamical systems using sparse Bayesian learning.
problem Creating and updating accurate digital twins for complex dynamical systems.
method Sparse Bayesian machine learning, two approaches: input-output and output-only.
result Identifies correct perturbation terms and associated parameters in dynamical systems.
Spectral gradient methods outperform Euclidean in certain deep learning scenarios.
problem When do spectral gradient updates outperform Euclidean in deep learning?
method Layerwise condition comparing squared nuclear-to-Frobenius ratio to stable rank of activations.
result Spectral updates can be more effective than Euclidean in deep networks and transformers.
Proposes a model for identifying edges in low-rank dynamical networks.
problem Inability of conventional methods to handle low-rank dynamical networks.
method Low rank dynamical network model with causal Wiener filtering.
result Consistent method for estimating all network edges.
A well-known problem in data science and machine learning is {\em linear regression}, which is recently extended to dynamic graphs. Existing exact algorithms for updating the solution of dynamic graph regression require at least a linear time (in terms of n: the size of the graph). However, this time complexity might…
This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each iteration, and each subspace update can be performed in linear time in the dimension of…
COLoKe adapts Koopman embeddings online, reducing overfitting and improving long-term predictions.
problem Online adaptation of Koopman embeddings to avoid overfitting and maintain long-term predictive accuracy.
method Combines deep feature learning with multistep prediction consistency in a lifted space, using a conformal-style mechanism for selective updates.
result Empirically effective in reducing overfitting and maintaining long-term predictive accuracy.
This paper analyzes how periodic and soft target updates stabilize linear Q-learning.
problem Theoretical explanation of stabilization mechanisms for linear Q-learning.
method Exact analysis using switched linear system dynamics and the joint spectral radius.
result Periodic and soft target updates can guarantee convergence to the exact projected Q-Bellman solution under specific conditions.
To continuously improve quality and reflect changes in data, machine learning applications have to regularly retrain and update their core models. We show that a differential analysis of language model snapshots before and after an update can reveal a surprising amount of detailed information about changes in the train…
Improves graph-based active learning for non-Gaussian models.
problem Efficiently selecting data points for labeling in graph-based semi-supervised learning.
method Approximates non-Gaussian distributions, introduces rank-one update and model change acquisition function.
result Enhanced active learning for graph-based SSL under non-Gaussian models.
This paper studies recursive ensembles driven by Fibonacci updates, improving learning dynamics.
problem Improving learning dynamics in recursive ensemble learning.
method Develops second-order recursive architectures with Fibonacci-type update flows.
result Establishes global convergence conditions and generalization bounds for recursive ensembles.
Games generalize the single-objective optimization paradigm by introducing different objective functions for different players. Differentiable games often proceed by simultaneous or alternating gradient updates. In machine learning, games are gaining new importance through formulations like generative adversarial netwo…
Efficiently completes low-rank matrices with nearly linear time complexity.
problem Completing low-rank matrices from a few observed entries.
method Robust alternating minimization framework with approximate updates.
result Achieves nearly linear time complexity in matrix completion.
Improved MORE algorithm reduces regret in black-box optimization and RL tasks.
problem Noisy fitness evaluations and poor sample quality in black-box optimization.
method Decouples mean and covariance updates, uses entropy scheduling, and simplifies model learning.
result Significantly reduces regret in black-box optimization and RL tasks.
GFM models neural network training as a dynamical system to forecast final weights.
problem Computational intensity and inefficiency in training deep neural networks.
method Gradient Flow Matching (GFM) treats training as a dynamical system with learned vector fields.
result GFM achieves forecasting accuracy competitive with Transformer-based models and significantly outperforms classical baselines.